MEXICO CITY, Mexico (CNN) -- The United States has withdrawn from an international agreement that gives the International Court of Justice the right to adjudicate violations of the Vienna Convention regarding the incarceration of non-U.S. citizens, U.S. Secretary of State Condoleeza Rice said Thursday.

Rice said the United States remains a signatory to the convention, which mandates that jailed foreigners have a right to see a diplomat from their home country, but has withdrawn from an optional protocol to the convention making the ICJ the arbiter of violations.

Last week, President Bush asked the state of Texas to order new hearings for 51 death row inmates from Mexico, as the ICJ had ordered.

"The decision the ICJ handed down is a decision we don't agree with," said State Department spokesman Adam Ereli in Washington. "Yet, in respect of the optional protocol and our international commitment, the president has determined that the United States will comply and our state courts will review the cases."

"But we're also saying in the future we're going to find other ways to resolve disputes under the Vienna Convention other than the ICJ," he said.

Ereli disputed that the decision to withdraw from the protocol is not an example of unilateralism or "cherry-picking" what international laws the United States will or won't abide by.

"I don't think anybody should conclude ... that we are any less committed to the international system or that we are in any way walking back from international community," he said. "To the contrary. We remain part of the Vienna Convention. We remain committed to fulfilling its provisions, and we stand by it."

Ereli said the United States, which ratified the convention in 1969, "never anticipated ... that the ICJ would be used to review cases of domestic criminal law."

"This is a really unexpected and unwelcome precedent where people who don't like decisions of our state courts can use an international court as their court of appeal," he said. "We have a system of justice that provides people with due process and review of their cases, and it's not appropriate that there should be some international court that comes in and reverses decision of our national courts."